Find an index i such that Arr [i] = i in array of n distinct integers sorted in ascending order.

Given an array of n distinct integers sorted in ascending order, write a function that returns a Fixed Point in the array such that Arr[i] = i .
If there is any Fixed Point present in array, else returns -1.
Note that integers in array can be negative.



Example :

  Input: arr[] = {-2, -1, 1, 3, 5}
  Output: 3  // arr[3] == 3 

  Input: arr[] = {-4, -1, 1, 2, 5, 8}
  Output: -1  // No Fixed Point

First Simple Method : Linear Search
for(i = 0; i < n; i++){
        if(arr[i] == i) return i;
}
Complexity O(n)

Method 2 : Divide and Conquer (As numbers is sorted we can use it as binary search)

Thanks to Dhaval for suggesting this Code.

int indexSearch(int arr[], int low, int high)
{
    if(high >= low)
    {
        int mid = (low + high)/2;
        if(mid == arr[mid])
            return mid;
        if(mid > arr[mid])
            return indexSearch(arr, (mid + 1), high);
        else
            return indexSearch(arr, low, (mid -1));
    }

    /* Return -1 if there is no Fixed Point */
    return -1;
}
int main()
{
    int arr[] = {-2, -1, 1, 3, 5};
    int n = sizeof(arr)/sizeof(arr[0]);
    printf("Fixed Point is %d", indexSearch(arr, 0, n-1));
    getchar();
    return 0;
}